Dilute antiferromagnetism and random fields in two-dimensional Ising systems

Abstract

We study the two-dimensional (2D) diluted antiferromagnet in a uniform magnetic field using the real-space renormalization group in a hierarchical cell. We follow separately the probability distributions of random-exchange couplings and of magnetic fields along the renormalization process. Due to the random couplings, the initial uniform magnetic field becomes a random variable with a mean value that continuously decreases to zero. In this 2D case the flow of the probability distributions is always toward the attractor of the paramagnetic phase characterized by 〈T/J〉=\ensuremath{\infty} and 〈(h/T${)}^{2}$〉=\ensuremath{\infty} in agreement with ${\mathit{d}}_{\mathit{c}}$=2. We discuss the connections of our results with those obtained previously for the random-field problem.